The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?
A.p(10⁴ − k²)² = q × 10⁸✓ Correct
B.p(10⁴ − k²)² = q × 10⁴
C.p(10⁴ − k²) = q × 10⁴
D.p(10⁴ − k²) = q × 10⁸
Explanation
After successive +k%, −k%, +k%, −k% changes, the multiplier is (1+k/100)(1−k/100)(1+k/100)(1−k/100) = [(1−k²/10⁴)]². So q = p × (1 − k²/10⁴)² = p × (10⁴ − k²)²/10⁸. Rearranging: p(10⁴ − k²)² = q × 10⁸. This matches option (a).
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